(a) On the set of people, (a, b) ∈R iff a and b both catch public transport  (b) On the set of 2D vectors, (u, v) ∈R iff u *  v = 0

Q: ▶Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, v3)…

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: - c(13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18) Fine the vector y by the…

A: year x 1951 13 1952 23 1953 21 1954 27 1955 37 1956 52 1957 34 1958 42 1959 31…

Q: What should k be if the vectors x=(1,1,k) y=(1,3,1) z=(k,1,3) are in the same plane in the Euclidean…

A: Three vector a1,a2,a3,b1,b2,b3 and c1,c2,c3 will be in euclidean space ℝ3 If  a1a2a3b1b2b3c1c2c3=0…

Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

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Q: 8) (True/False) Use the definition of linear independence to check whether the vectors u₁, u₂, and…

A: The given vectors are

Q: If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) ==…

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Q: (×q) × (gxv) + (gxg) x (xv) + (x) x (qxv)

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Q: Let W be the set of all vectors of the form ū = H V = [-5s- 2t] 5s + 3t 5s + t . Find vectors ū and…

A: Let S={u,v} be a linear independent set and generate W . Then W=span{u,v} .

Q: If V₁, V2 and v3 are 3 vectors in a vector space V such that -7v₁-9v2 = 0. V, and v₂ are linearly…

A: Given that v1, v2, and v3 are 3 vectors in a vector space Vsuch that -7v1-9v2=0. Then v1, v2,and v3…

Q: The two vectors u=(-2,3,1,4) and v= (1,2,0, -1) are orthogonal in the vector space R4 True False

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Q: If vectors b, c and d are not coplanc then prove that vector

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Q: Find all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

Q: the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V, + 5v), v =…

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Q: Let a and b be vectors in R" such that ||a||=|| b||=2 and (a,b)= — . Then ||a - b||= ...

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Q: Suppose a, b, c are vectors in R³ for which Then (22a) ((14b) x (10c)) = Check det[a b c] = 2 Which…

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Q: 5- Suppose that A = {x1 = (3,1,2), x2 = (0,0,2), x3 = (2,0,1)} then [A] = R³, that means for every…

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Q: 6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are linear…

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A: Given three vectors which span w.

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: Let v1, V2, V3 and u be vectors in R". If u is orthogonal to each of v1, V2, and v3 then u is…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (V2 - V, V1 + V2,…

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Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: Mickey Mantle played for the New York Yankees for 18 years from 1951 to 1968. Year by year he hit…

A: Note: As per the guidelines only three sub-parts can be answered. Kindly, repost for other parts.

Q: 7) Find all vectors v in F such that 2v + ) -)

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 V1, V1 + V2,…

A: Let us consider the transformation T: V→W defined as T(v)=w where v is preimage of w  and w is an…

Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such…

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Q: Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1,-1,2) 11.- Define the…

A: The given vectors .The aim is to find the norm of the vector .